Abrikosov vortex lattice

Nb thin films have been deposited on porous silicon (PS) substrates. The PS templates consists of a short-range order matrix of pores with mean diameter of 10 nm and mean interpore distance of 40 nm, which act as an array of artificial pinning centers. Commensurability effects between the Abrikosov vortex lattice and the artificial one were investigated by transport measurements. 

The development of patterns is not necessarily a manifestation of a nonequilibrium process. A spatially non-uniform state can correspond to the minimum of the free-energy functional of a system in thermodynamic equihbrium, as Abrikosov vortex lattices, stripe ferromagnetic phases and periodic diblock-copolymer phases mentioned above. In the latter, a hnear chain molecule of a diblock-copolymer consists of two blocks, say, A and B. Above the critical temperature Tc, there is a mixture of both types of blocks. Below Tc, the copolymer melt undergoes phase separation that leads to the formation of A-rich and B-rich microdomains. In the bulk, these microdomains typically have the shape of lamellae, hexagonally ordered cylinders or body-centered cubic (bee) ordered spheres. On the surface, one again observes stripes or hexagonally ordered spots. 

Twist grain boundary (TGB) phase Shubnikov phase / Abrikosov vortex lattice... 

We have studied both static and dynamic properties of the vortex systems, such as Abrikosov vortex lattice formation, vortex lattice melting, the KT transition, and the vortex glass transition, from the point of view of an analogy between our system and colloid, polymer systems [3]. Our study is based on computer simulations of two efficient model equations, recently developed by us. 

Abrikosov flux lattice 333 observed by STM 333 tunneling conductance near a vortex 334 AFM... 

In condensed matter physics, the effects of disorder, defects, and impurities are relevant for many materials properties hence their understanding is of utmost importance. The effects of randomness and disorder can be dramatic and have been investigated for a variety of systems covering a wide field of complex phenomena [109]. Examples include the pinning of an Abrikosov flux vortex lattice by impurities in superconductors [110], disorder in Ising magnets [111], superfluid transitions of He in a porous medium [112], and phase transitions in randomly confined smectic liquid crystals [113, 114]. 

Next came the likewise phenomenological Ginzburg-Landau theory of superconductivity, based on the Landau theory of a second-order phase transition (see also Appendix B) that predicted the coherence length and penetration depth as two characteristic parameters of a superconductor (Ginzburg and Landau, 1950). Based on this theory, Abrikosov derived the notion that the magnetic field penetrates type II superconductors in quantized flux tubes, commonly in the form of a hexagonal network (Abrikosov, 1957). The existence of this vortex lattice was... 

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